Portable Applications (or PA for short) already has portable Firefox and portable Firefox Beta. A few other websites also create their own packages, including Nightly builds, to be installed in your portable app folder. But, PA does not support Firefox Nightly build. So you have to do it yourself.

There is a page on the PA forums that tells you what to do in order to install your own portable Firefox Nightly build. and here is what it says:

You downloaded Process Explorer and examined every single process running in memory to find a sign of a program that may be using _something_ in that folder. You closed all programs, every resident applications, and all running processes that can be closed. You also closed even some of Windows process and stopped as many services as possible; no sign of any file handle to anything related to that folder… result: negative.

You have uninstalled many programs that you suspect they may cause the problem;… negative.

You did chkdskc: /f, RegSeeker, NortonDiskDoctor, Regedit (see also this), and lots of command line instructions that you read in forums;… negative (in regedit, you cannot even see any entry with the same name as that stupid file in your Windows registry.) (more about chkdsk.)